Velocity sonic

K = Cp/Cv the ratio of specific heats at constant pressure to constant volume. This ratio is 1.4 for most diatomic gases, g = 32.2 ft/sec  

To determine the critical pressure ratio for gas sonic velocity across a nozzle or orifice use 

If pressure drop is high enough to exceed the critical ratio, sonic velocity will be reached. When K = 1.4, ratio = 0.53. 

Branan, C. R., The. Process Engineer s Pocket Handbook, Vol. 1, Gulf Publishing Co., 1976. 

Uo = Velocity through orifice, ft/sec Up = Velocity through pipe, ft/sec 

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The basics of the method are simple. Reflections occur at all layers in the subsurface where an appreciable change in acoustic impedance is seen by the propagating wave. This acoustic impedance is the product of the sonic velocity and density of the formation. There are actually different wave types that propagate in solid rock, but the first arrival (i.e. fastest ray path) is normally the compressional or P wave. The two attributes that are measured are... 

The flow velocity is thus proportional to the difference in transit time between the upstream and downstream directions and to the square of the speed of sound in the fluid. Because sonic velocity varies with fluid properties, some designs derive compensation signals from the sum of the transit times which can also be shown to be proportional to C. 

In the manufacture of meltblown fabrics, a special die is used in which heated, pressurized air attenuates the molten polymer filament as it exits the orifice of the dye or nozzle (Fig. 9). Air temperatures range from 260—480°C with sonic velocity flow rates (43). 

The AeroSizer, manufactured by Amherst Process Instmments Inc. (Hadley, Massachusetts), is equipped with a special device called the AeroDisperser for ensuring efficient dispersal of the powders to be inspected. The disperser and the measurement instmment are shown schematically in Figure 13. The aerosol particles to be characterized are sucked into the inspection zone which operates at a partial vacuum. As the air leaves the nozzle at near sonic velocities, the particles in the stream are accelerated across an inspection zone where they cross two laser beams. The time of flight between the two laser beams is used to deduce the size of the particles. The instmment is caUbrated with latex particles of known size. A stream of clean air confines the aerosol stream to the measurement zone. This technique is known as hydrodynamic focusing. A computer correlation estabUshes which peak in the second laser inspection matches the initiation of action from the first laser beam. The equipment can measure particles at a rate of 10,000/s. The output from the AeroSizer can either be displayed as a number count or a volume percentage count. 

Descriptions of sulfuric acid analytical procedures not specified by ASTM are available (32,152). Federal specifications also describe the requited method of analysis. Concentrations of 78 wt % and 93 wt % H2SO4 are commonly measured indirectly by determining specific gravity. Higher acid concentrations are normally determined by titration with a base, or by sonic velocity or other physical property for plant control. Sonic velocity has been found to be quite accurate for strength analysis of both filming and nonfuming acid. 

Note that under choked conditions, the exit velocity is V = V = c = V/cKTVM not V/cKT(/M, . Sonic velocity must be evaluated at the exit temperature. For air, with k = 1.4, the critical pressure ratio p /vo is 0.5285 and the critical temperature ratio T /Tq = 0.8333. Thus, for air discharging from 300 K, the temperature drops by 50 K (90 R). This large temperature decrease results from the conversion of internal energy into kinetic energy and is reversible. As the discharged jet decelerates in the external stagant gas, it recovers its initial enthalpy. 

Velocity meters with density compensation. The signal from the velocity meter (e.g., turbine meter, electromagnetic meter, or sonic velocity meter) is multiplied by the signal from a densitometer to give a signal proportional to the mass flow rate. 

Deflagration A propagating chemical reaction of a substance in which the reaction front advances into the unreacted substance at less than the sonic velocity in the unreacted material. Where a blast wave is produced that has the potential to cause damage, the term explosive deflagration may be used. 

For compressible fluids one must be careful that when sonic or choking velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very liigh. See Sonic Velocity later in this chapter. 

This will give a conservative relief valve area. For compressible fluids use Ah corresponding to lAPi if head difference is greater than that corresponding to Pi (since sonic velocity occurs). If head difference is below that corresponding to APi use actual Ah. 

Eor good control, design the pressure drop for the control valve between the fractionating system and the jet system for sonic velocity (approximately 2 1 pressure ratio). This means that the jets suction must be designed for half the absolute pressure of the evacuated system. 

Calculate the sonic velocity using Equation 2.32 where... 

This is a low value, therefore, the possibility exists of an up-rate relative to any nozzle flow limits. At this point, a comment or two is in order. There is a rule of thumb that sets inlet nozzle velocity limit at approximately 100 fps. But because the gases used in the examples have relatively high acoustic velocities, they will help illustrate how this limit may be extended. Regardless of the method being used to extend the velocity, a value of 150 fps should be considered maximum. When the sonic velocity of a gas is relatively low, the method used in this example may dictate a velocity for the inlet nozzle of less than 100 fps. The pressure drop due to velocity head loss of the original design is calculated as follows ... 

Step 2, Reuse the rotor tip speed and sonic velocity from Example 4-1 as the conditions used in their development that have not changed. 

As normally designed, vapor flow through a typical high-lift safety reliefs valve is characterized by limiting sonic velocity and critical flow pressure conditions at the orifice (nozzle throat), and for a given orifice size and gas composition, mass flow is directly proportional to the absolute upstream pressure. 

Since the pressure drop is quite high, there is a possibility of approaching sonic velocity in the line. This will result in a potential noise problem. Hence, it is a good practice to limit the velocity to 60 percent of the sonic velocity or a 0.6 Mach number. 

As a first trial, an inside pipe diameter is assumed based on 60 percent of the sonic velocity corresponding to the pressure and temperature at the base of the stack, i.e., at 2 psig and temperature =T (upstream temperature since isothermality is assumed). 

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